Definition
Rhombus.jpg

Rhombus is a kite with opposite parallel sides






Properties
Side Properties
1. All sides are congruent
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Angle Properties
1. Consecutive angles are supplementary
Rhombus_3.jpg
Example Proof
Prove: Angle HOm and Angle MOI are supplementary

Rhombus_11.jpg





Diagonal Properties
1. Diagonals bisect each other
Rhombus_7.jpg



2. *Diagonals bisect the angles

Rhombus_9.jpg

This is the most important property of a rhombus for the following reasons:

- Knowing that these diagonals bisect the angles, we can identify triangles (Triangle RHO, Triangle RMO, Triangle HOM, Triangle HRM) as isosceles, and use properties of isosceles to find unknown side and angle measures
- Knowing that these diagonals bisect the angles, congruence of oppositely oriented triangles can be proved using triangle congruence shortcuts